Question

Log(1/6)36 what is the answer its not 6???

Answer 1

turn it into exponent form, so Log(1/6)36 ⇒ (1/6)^x=36
1. 6²=36
2. (1/6)²=(1²/6²)=1/36
so Log(1/6)36=2
:) hope that helped...

Answer 2

`\text{log}_{(1)/(6)}(36)=-2`

Explanation:

We have been given a logarithm expression
`\text{log}_{(1)/(6)}(36)`. We are asked to evaluate our given expression.

Using logarithm rule
`log_{(1)/(a)}(x)=-log_a(x)`, we can write our expression as:

`\text{log}_{(1)/(6)}(36)=-\text{log}_6(36)`

`\text{log}_{(1)/(6)}(36)=-\text{log}_6(6^2)`

Using logarithm rule
`\text{log}_(a)(x^b)=b\text{log}_a(x)`, we will get:

`\text{log}_{(1)/(6)}(36)=-2\text{log}_6(6)`

Applying rule
`\text{log}_(a)(a)=1`, we will get:

`\text{log}_{(1)/(6)}(36)=-2\cdot 1`

`\text{log}_{(1)/(6)}(36)=-2`

Therefore,
`\text{log}_{(1)/(6)}(36)=-2`.